How to make python script check some value every frame
After a lot of googling, combining scraps of code and testing, I finally found the solution for this issue.I'm leaving it here cause it actually can be pretty useful in some situations.

See the docs about event handlers 

import bpy
import math

sce = bpy.data.scenes[0]

# the function to call whenever the handler is envoked
def my_handler(sce):
    # contObj is controlling object, the one, which world Z position
    # I take to control rotation of "Target"
    contObj = bpy.data.objects["Controler"]

    # posOnZ is rounded world Z position of contObj 
    posOnZ = round(contObj.matrix_world.to_translation().z,3)

    # targObj is the object, which rotation will be changed, when posOnZ reach
    # certain value.
    targObj = bpy.data.objects["Target"]

    if posOnZ == 1.168:
        targObj.rotation_euler[2]+=6*(math.pi/180)

        # check if everything works (can be omitted)
        print(targObj.rotation_euler[2]*(180/math.pi) )

        #without sce.update() you can't see the changes in 3d view
        sce.update()

def register():
    bpy.app.handlers.frame_change_pre.append(my_handler)

my_handler(sce)  # optional, to test if the function is working..

register()